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Format: 1 online resource (649 pages)

Edition: 1st ed.

ISBN: 9780521781718 , 9780511156601

Content: This comprehensive text and reference, first published in 2002, combines the theory behind financial engineering with numerous algorithms for pricing, risk management, and portfolio management. It offers a thorough grounding in the subject for students and researchers in computational finance, system analysts, and financial engineers. Java programs for the Web are available from the book's home page

Note: Cover -- Half-title -- Title -- Copyright -- Dedication -- Contents -- Preface -- Intended Audience -- Presentation -- Software -- Organization -- Acknowledgments -- Useful Abbreviations -- Acronyms -- Ticker Symbols -- CHAPTER ONE Introduction -- 1.1 Modern Finance: A Brief History -- 1.2 Financial Engineering and Computation -- 1.3 Financial Markets -- 1.4 Computer Technology -- NOTES -- CHAPTER TWO Analysis of Algorithms -- 2.1 Complexity -- 2.2 Analysis of Algorithms -- 2.3 Description of Algorithms -- 2.4 Software Implementation -- NOTE -- CHAPTER THREE Basic Financial Mathematics -- 3.1 Time Value of Money -- 3.1.1 Efficient Algorithms for Present and Future Values -- 3.1.2 Conversion between Compounding Methods -- 3.1.3 Simple Compounding -- 3.2 Annuities -- 3.3 Amortization -- 3.4 Yields -- 3.4.1 Internal Rate of Return -- 3.4.2 Net Present Value -- 3.4.3 Numerical Methods for Finding Yields -- The Bisection Method -- The Newton-Raphson Method -- 3.4.4 Solving Systems of Nonlinear Equations -- 3.5 Bonds -- 3.5.1 Valuation -- 3.5.2 Price Behaviors -- 3.5.3 Day Count Conventions -- 3.5.4 Accrued Interest -- 3.5.5 Yield for a Portfolio of Bonds -- 3.5.6 Components of Return -- Additional Reading -- NOTES -- CHAPTER FOUR Bond Price Volatility -- 4.1 Price Volatility -- 4.2 Duration -- 4.2.1 Continuous Compounding -- 4.2.2 Immunization -- 4.2.3 Macaulay Duration of Floating-Rate Instruments -- 4.2.4 Hedging -- 4.3 Convexity -- Additional Reading -- NOTE -- CHAPTER FIVE Term Structure of Interest Rates -- 5.1 Introduction -- 5.2 Spot Rates -- 5.3 Extracting Spot Rates from Yield Curves -- 5.4 Static Spread -- 5.5 Spot Rate Curve and Yield Curve -- 5.6 Forward Rates -- 5.6.1 Locking in the Forward Rate -- 5.6.2 Term Structure of Credit Spreads -- 5.6.3 Spot and Forward Rates under Continuous Compounding , 17.3 Pricing Multivariate Contingent Claims , 5.6.4 Spot and Forward Rates under Simple Compounding -- 5.7 Term Structure Theories -- 5.7.1 Expectations Theory -- Unbiased Expectations Theory -- Other Versions of the Expectations Theory -- 5.7.2 Liquidity Preference Theory -- 5.7.3 Market Segmentation Theory -- 5.8 Duration and Immunization Revisited -- 5.8.1 Duration Measures -- 5.8.2 Immunization -- The Case of NO Rate Changes -- The Case of Certain Rate Movements -- Additional Reading -- NOTES -- CHAPTER SIX Fundamental Statistical Concepts -- 6.1 Basics -- 6.1.1 Generalization to Higher Dimensions -- 6.1.2 The Normal Distribution -- 6.1.3 Generation of Univariate and Bivariate Normal Distributions -- 6.1.4 The Lognormal Distribution -- 6.2 Regression -- 6.3 Correlation -- 6.4 Parameter Estimation -- 6.4.1 The Least-Squares Method -- 6.4.2 The Maximum Likelihood Estimator -- 6.4.3 The Method of Moments -- Additional Reading -- NOTES -- CHAPTER SEVEN Option Basics -- 7.1 Introduction -- 7.2 Basics -- 7.3 Exchange-Traded Options -- 7.4 Basic Option Strategies -- 7.4.1 Hedge -- 7.4.2 Spread -- 7.4.3 Combination -- NOTES -- CHAPTER EIGHT Arbitrage in Option Pricing -- 8.1 The Arbitrage Argument -- 8.2 Relative Option Prices -- 8.3 Put-Call Parity and Its Consequences -- 8.4 Early Exercise of American Options -- 8.5 Convexity of Option Prices -- 8.6 The Option Portfolio Property -- Concluding Remarks and Additional Reading -- CHAPTER NINE Option Pricing Models -- 9.1 Introduction -- 9.2 The Binomial Option Pricing Model -- 9.2.1 Options on a Non-Dividend-Paying Stock: Single Period -- 9.2.2 Risk-Neutral Valuation -- 9.2.3 Options on a Non-Dividend-Paying Stock: Multiperiod -- A Numerical Example -- 9.2.4 Numerical Algorithms for European Options -- Binomial Tree Algorithms -- An Optimal Algorithm -- The Monte Carlo Method -- The Recursive Formulation and Its Algorithms , 9.3 The Black-Scholes Formula -- 9.3.1 Distribution of the Rate of Return -- 9.3.2 Toward the Black-Scholes Formula -- Tabulating Option Values -- 9.3.3 The Black-Scholes Model and the BOPM -- 9.4 Using the Black-Scholes Formula -- 9.4.1 Interest Rate -- 9.4.2 Estimating the Volatility from Historical Data -- 9.4.3 Implied Volatility -- 9.5 American Puts on a Non-Dividend-Paying Stock -- 9.6 Options on a Stock that Pays Dividends -- 9.6.1 European Options on a Stock that Pays a Known Dividend Yield -- 9.6.2 American Options on a Stock that Pays a Known Dividend Yield -- 9.6.3 Options on a Stock that Pays Known Dividends -- A Simplifying Assumption -- 9.6.4 Options on a Stock that Pays a Continuous Dividend Yield -- 9.7 Traversing the Tree Diagonally -- Additional Reading -- NOTES -- CHAPTER TEN Sensitivity Analysis of Options -- 10.1 Sensitivity Measures ("The Greeks") -- 10.1.1 Delta -- 10.1.2 Theta -- 10.1.3 Gamma -- 10.1.4 Vega -- 10.1.5 Rho -- 10.2 Numerical Techniques -- 10.2.1 Why Numerical Differentiation Fails -- 10.2.2 Extended Binomial Tree Algorithms -- NOTE -- CHAPTER ELEVEN Extensions of Options Theory -- 11.1 Corporate Securities -- 11.1.1 Risky Zero-Coupon Bonds and Stock -- Numerical Illustrations -- Conflicts between Stockholders and Bondholders -- Subordinated Debts -- 11.1.2 Warrants -- 11.1.3 Callable Bonds -- 11.1.4 Convertible Bonds -- Convertible Bonds with Call Provisions -- 11.2 Barrier Options -- 11.2.1 Bonds with Safety Covenants -- 11.2.2 Nonconstant Barrier -- 11.2.3 Other Types of Barrier Options -- 11.3 Interest Rate Caps and Floors -- 11.4 Stock Index Options -- 11.5 Foreign Exchange Options -- 11.5.1 The Black-Scholes Model for Forex Options -- 11.5.2 Some Pricing Relations -- 11.6 Compound Options -- 11.7 Path-Dependent Derivatives -- Additional Reading -- NOTES , CHAPTER TWELVE Forwards, Futures, Futures Options, Swaps -- 12.1 Introduction -- 12.2 Forward Contracts -- 12.2.1 Forward Exchange Rate -- Spot and Forward Exchange Rates -- 12.2.2 Forward Price -- The Underlying Asset Pays No Income -- The Underlying Asset Pays Predictable Income -- The Underlying Asset Pays a Continuous Dividend Yield -- 12.3 Futures Contracts -- 12.3.1 Daily Cash Flows -- 12.3.2 Forward and Futures Prices -- 12.3.3 Stock Index Futures -- 12.3.4 Forward and Futures Contracts on Currencies -- 12.3.5 Futures on Commodities and the Cost of Carry -- 12.4 Futures Options and Forward Options -- 12.4.1 Pricing Relations -- 12.4.2 The Black Model -- 12.4.3 Binomial Model for Forward and Futures Options -- 12.5 Swaps -- 12.5.1 Currency Swaps -- 12.5.2 Valuation of Currency Swaps -- As a Package of Cash Market Instruments -- As a Package of Forward Contracts -- Additional Reading -- NOTES -- CHAPTER THIRTEEN Stochastic Processes and Brownian Motion -- 13.1 Stochastic Processes -- 13.2 Martingales ("Fair Games") -- 13.2.1 Martingale Pricing and Risk-Neutral Valuation -- 13.2.2 Futures Price under the Binomial Model -- 13.2.3 Martingale Pricing and the Choice of Numeraire -- 13.3 Brownian Motion -- 13.3.1 Brownian Motion as the Limit of a Random Walk -- 13.3.2 Geometric Brownian Motion -- 13.3.3 Stationarity -- 13.3.4 Variations -- 13.4 Brownian Bridge -- Additional Reading -- NOTES -- CHAPTER FOURTEEN Continuous-Time Financial Mathematics -- 14.1 Stochastic Integrals -- 14.2 Ito Processes -- 14.2.1 Discrete Approximations -- 14.2.2 Trading and the Ito Integral -- 14.2.3 Ito's Lemma -- 14.3 Applications -- 14.3.1 The Ornstein-Uhlenbeck Process -- 14.3.2 The Square-Root Process -- 14.4 Financial Applications -- 14.4.1 Transactions Costs -- 14.4.2 Stochastic Interest Rate Models -- The Merton Model -- Duration under Parallel Shifts , Immunization under Parallel Shifts Revisited -- 14.4.3 Modeling Stock Prices -- Continuous-Time Limit of the Binomial Model -- Additional Reading -- NOTE -- CHAPTER FIFTEEN Continuous-Time Derivatives Pricing -- 15.1 Partial Differential Equations -- 15.2 The Black-Scholes Differential Equation -- 15.2.1 Merton's Derivation -- Continuous Adjustments -- Number of Random Sources -- Risk-Neutral Valuation -- 15.2.2 Solving the Black-Scholes Equation for European Calls -- 15.2.3 Initial and Boundary Conditions -- 15.3 Applications -- 15.3.1 Continuous Dividend Yields -- 15.3.2 Futures and Futures Options -- 15.3.3 Average-Rate and Average-Strike Options -- 15.3.4 Options on More than One Asset: Correlation Options -- 15.3.5 Exchange Options -- 15.3.6 Options on Foreign Currencies and Assets -- Foreign Equity Options -- Foreign Domestic Options -- Cross-Currency Options -- Quanto Options -- 15.3.7 Convertible Bonds with Call Provisions -- 15.4 General Derivatives Pricing -- 15.5 Stochastic Volatility -- Additional Reading -- NOTE -- CHAPTER SIXTEEN Hedging -- 16.1 Introduction -- 16.2 Hedging and Futures -- 16.2.1 Futures and Spot Prices -- 16.2.2 Hedgers, Speculators, and Arbitragers -- 16.2.3 Perfect and Imperfect Hedging -- Cross Hedge -- Hedge Ratio (Delta) -- 16.2.4 Hedging with Stock Index Futures -- 16.3 Hedging and Options -- 16.3.1 Delta Hedge -- A Numerical Example -- 16.3.2 Delta-Gamma and Vega-Related Hedges -- 16.3.3 Static Hedging -- Additional Reading -- NOTE -- CHAPTER SEVENTEEN Trees -- 17.1 Pricing Barrier Options with Combinatorial Methods -- 17.1.1 The Reflection Principle -- 17.1.2 Combinatorial Formulas for Barrier Options -- 17.1.3 Convergence of Binomial Tree Algorithms -- 17.1.4 Double-Barrier Options -- 17.2 Trinomial Tree Algorithms -- 17.2.1 Pricing Barrier Options -- 17.2.2 Remarks on Algorithm Comparison

Additional Edition: Print version Lyuu, Yuh-Dauh Financial Engineering and Computation Cambridge : Cambridge University Press,c2001 ISBN 9780521781718

Language: English

Keywords: Electronic books

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